Lots o fixes

Author: scheinerman

README.md

@@ -15,10 +15,11 @@ At present it will fail if:
 * The LP is unbounded.
 * Other unidentified reasons. (In other words, still buggy.)
 
-It is also set up for maximization problems only. To solve a minimization problem use the dual LP by
-replacing the inputs `A`, `b`, and `c` with `A'`, `c`, and `b` respectively. 
 
+This module also set up for maximization problems only. To solve a minimization problem use the dual LP by
+replacing the inputs `A`, `b`, and `c` with `A'`, `c`, and `b` respectively. 
 
+This module solves LPs using the simplex algorithm which is not the most performant method. Further, all data is stored using arbitrary precision integers (that is, `Rational{BigInt}`) which gives exact answer, but is much slower than floating point arithmetic. These issues are negligible for small problems. 
 
 
 # Quick Start Instructions

docs/build/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.11.4","generation_timestamp":"2025-04-03T14:22:49","documenter_version":"1.10.0"}}
+{"documenter":{"julia_version":"1.11.4","generation_timestamp":"2025-04-03T17:53:48","documenter_version":"1.10.0"}}

docs/build/index.html

@@ -2,4 +2,4 @@
 # Project: SimpleTableaux
 # Version: 0.0.2
 # The remainder of this file is compressed using zlib.
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docs/build/objects.inv

@@ -1,7 +1,5 @@
 # SimpleTableaux
 
-
-
 This is an illustration project for solving 
 feasible optimization problems (Linear Programs) of the form 
 $\max c^t x$ subject to $Ax ≤ b$ and $x \ge 0$.
@@ -123,7 +121,7 @@ julia> lp_solve(T)
  1.599999999999999
 ```
 
-## The `restore!` function
+## The `restore!` Function
 
 As mentioned, the `pivot!` and `pivot_solve!` functions modify the `Tableau`. Use `restore!` to return a `Tableau` to its original state like this: `restore!(T)`. 
 
@@ -174,4 +172,34 @@ julia> visualize(T)
 ```
 
 
-![](visual.png)
+![](visual.png)
+
+## Changing the Display Format
+
+The usual way a `Tableau` is printed looks like this:
+```
+4×7 DataFrame
+ Row │ x1     x2     s1     s2     s3     val    RHS   
+     │ Exact  Exact  Exact  Exact  Exact  Exact  Exact 
+─────┼─────────────────────────────────────────────────
+   1 │ 8      3      1      0      0      0      24
+   2 │ 1      1      0      1      0      0      4
+   3 │ 1      4      0      0      1      0      12
+   4 │ -2     -1     0      0      0      1      0
+```
+
+The column headings are (should be) self-explanatory. As usual we begin with the LP variables, $x_1$, $x_2$, and so forth (rendered as `x1`, `x2`, etc.), and then the slack variables, and the right hand side. There are no row labels. To remedy that, set the (nonexported) variable `SimpleTableaux.show_row_labels` to true.
+```
+julia> SimpleTableaux.show_row_labels=true;
+
+julia> T
+4×8 DataFrame
+ Row │ Row Name  x1     x2     s1     s2     s3     val    RHS   
+     │ String    Exact  Exact  Exact  Exact  Exact  Exact  Exact 
+─────┼───────────────────────────────────────────────────────────
+   1 │ cons1     8      3      1      0      0      0      24
+   2 │ cons2     1      1      0      1      0      0      4
+   3 │ cons3     1      4      0      0      1      0      12
+   4 │ obj       -2     -1     0      0      0      1      0
+```
+We now see that rows 1, 2, and 3 correspond to constraints and row 4 to the objective function. 

docs/build/search_index.js

@@ -1,3 +1,5 @@
+show_row_labels::Bool = false
+
 """
     DataFrame(T::Tableau)
 
@@ -6,10 +8,12 @@ Present a `Tableau` as a `DataFrame`.
 function DataFrame(T::Tableau)
     df = DataFrame()
 
-    # # Name the rows
-    # rownames = ["cons" * string(k) for k in 1:(T.n_cons)]
-    # push!(rownames, "obj")
-    # df[:, "Row Name"] = rownames
+    if show_row_labels
+        # Name the rows
+        rownames = ["cons" * string(k) for k in 1:(T.n_cons)]
+        push!(rownames, "obj")
+        df[:, "Row Name"] = rownames
+    end
 
     # Variable columns
     for i in 1:(T.n_vars)

docs/src/index.md

@@ -10,6 +10,26 @@ function find_pivot_column(T::Tableau)
     return v < 0 ? j : 0
 end
 
+"""
+    find_least_nonnegative(v::Vector)
+
+Find the index of the least nonnegative entry in `v` or `0` if all entries are negative. 
+"""
+function find_least_nonnegative(v::Vector)
+    m = maximum(v)
+    if m < 0
+        return 0  # no nonegative values
+    end
+    idx = 0
+    for k in 1:length(v)
+        if v[k] >= 0 && v[k] < m
+            m = v[k]
+            idx = k
+        end
+    end
+    return idx
+end
+
 """
     find_pivot_row(T::Tableau, j::Int)
 
@@ -19,7 +39,8 @@ function find_pivot_row(T::Tableau, j::Int)
     rhs = T.M[1:(end - 1), end]
     col = T.M[1:(end - 1), j]
     vals = rhs .// col
-    _, i = findmin(vals)
+    # _, i = findmin(vals)
+    i = find_least_nonnegative(vals)
     return i
 end
 

src/DataFrame.jl

@@ -45,7 +45,7 @@ struct Tableau
         end
         body = hcat(A, Matrix(I, m, m), zeros(Int, m), b)
 
-        obj = [-c; zeros(Int, m); 1; 0]'
+        obj = collect([-c; zeros(Int, m); 1; 0]')
 
         return new(vcat(body, obj), A, b, c, n, m)
     end
@@ -69,8 +69,9 @@ Restore a `Tableau` based on the original data used to create it.
 """
 function restore!(T::Tableau)
     TT = restore(T)
-    for i in 1:(T.n_cons)
-        for j in 1:(T.n_vars)
+    m, n = size(TT.M)
+    for i in 1:m
+        for j in 1:n
             T.M[i, j] = TT.M[i, j]
         end
     end

src/Pivoting.jl

@@ -0,0 +1,17 @@
+using SimpleTableaux
+
+"""
+    bad()
+
+Create a `Tableau` that `pivot_solve` can't handle. 
+"""
+function bad()
+    A = [
+        2 2 6
+        3 9 8
+        9 7 3
+    ]
+    b = [9; 1; 2]
+    c = [2; 1; 4]
+    return Tableau(A, b, c)
+end